Anomalous dielectric behaviour during the monoclinic to tetragonal phase transition in La(Nb_0.9V_0.1)O₄

Abstract

La(Nb_0.9V_0.1)O₄ has been shown by in situ Raman spectroscopy and X-ray diffraction to undergo a ferroelastic phase transition from monoclinic fergusonite to tetragonal scheelite (T_M–T) at 350 °C, accompanied by 3.55% spontaneous strain and an abrupt change in the thermal expansion coefficient (α_L) from +15.5 ppm °C⁻¹ to +11.4 ppm °C⁻¹. Assuming a linear relationship between polarizability and temperature, an anomalous decrease in relative permittivity (ε_r) at T_M–T is predicted from the Clausius–Mosotti relation and Shannon's additive rule. Such an anomalous decrease in ε_r in a phase transition has not previously been observed in ferroic and linear dielectrics and may aid in the design of novel microwave dielectric composites.

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Introduction

Microwave (MW) dielectric ceramic materials are widely used as dielectric resonators, filters, antenna substrates, and capacitors for wireless and mobile communication, and radar and satellite positioning systems.^1–4 The large ε_r (real part of permittivity) of MW dielectric ceramic materials helps in reducing the dimensions of MW devices and the low dielectric loss (high quality factor, Q) enhances the frequency selectivity.^2–5 Furthermore, their temperature stability with respect to resonant frequency (TCF) ensures that related devices work from −45 to 85 °C. 5th generation wireless systems (5G) have gradually come on-line in recent years and offer ultra-wideband, ultra-high speed, and ultra-low latency.^6–8 The frequency spectrum of 5G is generally divided into millimeter wave, mid-band and low-band. The millimeter wave (above 24 GHz) is yet to be exploited but materials with ε_r < 10 are likely to be utilised.^7–10 Low-band refers to available frequency ranges at <1 GHz, whereas mid-band exploits the 2–6 GHz interval and is the most widely deployed. To attain the required data transmission rates, massive MIMO (multiple input and multiple output) and Multi-User MIMO (MU-MIMO) antennas are employed that are composed of large numbers of interconnected devices.^11–15 Massive MIMO functions through mini base stations and exploits materials with ε_r = 20, such as MgTiO₃–CaTiO₃, (Ca_1+xSm_1−x)(Al_1−xTi_x)O₄, and Li₂TiO₃ due to their high Q and low TCF.^7,16–19

Alongside the three materials mentioned above, fergusonite-structured LnNbO₄ (Ln = La, Sm, Nd etc.) ceramics have attracted attention due to their high Q and ε_r ∼ 20.^20–23 Kim et al. first reported the microwave dielectric properties of LaNbO₄ ceramic sintered at 1250 °C with ε_r = 19.3, a high Qf (Q × resonant frequency, f) ∼ 54 400 GHz and TCF = +9 ppm °C⁻¹.²⁰ Substitutions of La or Nb by isovalent ions plus the use of sintering aid in further improving the microwave dielectric properties.^21–23 In our previous work,²¹ we demonstrated that 10 mol% substitution of V⁵⁺ for Nb⁵⁺ increases the TCF from +9 ppm °C⁻¹ to +110 ppm °C⁻¹.

TCF is approximately half the temperature coefficient ε_r (τ_ε) according to:

where α_l is the linear thermal expansion coefficient (below +15 ppm °C⁻¹ for ceramics). Hence, any abrupt change in TCF is normally attributed to a change in τ_ε usually caused by a structural phase transition. Phase transitions which show an increase in ε_r are commonplace in ferroic materials as commonly observed for paraelectric to ferroelectric/antiferroelectric, ferroelectric to ferroelectric, octahedral tilt and paraelastic to ferroelastic transformations.^24–31

All the above phase transitions occur through classical softening of a transverse optical mode, consistent with the Lyddane–Sach–Teller relation.³² Since the maximum value of ε_r occurs at the phase transition temperature (PTT/T_C), τ_ε is largely positive below, but negative above the PTT, provided ε_r is not too high. This principle is the basis for the well-established relationship between the tolerance factor and τ_ε described by Reaney et al.³³ in which octahedral tilting induces an increase in ε_r at the PTT in Sr- and Ba-based complex perovskites. The TCF follows the inverse trend. Similarly BiVO₄ undergoes a second-order ferroelastic phase transition from the monoclinic (I2/a) to tetragonal scheelite (I4₁/a) structure at 255 °C, at which temperature a maximum value of ε_r is observed.^31,34–38 Furthermore in (Li_0.5xBi_1−0.5x)(Mo_xV_1−x)O₄ (0 ≤ x ≤ 0.25) ceramics, peaks in ε_r are observed at the PTT^38,39 with the corresponding changes in TCF.

LaNbO₄ also undergoes a ferroelastic phase transition from a monoclinic fergusonite to tetragonal scheelite structure at ∼480 °C.^40–45 From previous studies,^21,46 V⁵⁺ substitutes for Nb⁵⁺ on the B site and lowers the PTT to room temperature, where the tetragonal scheelite structure is stabilized for x = 0.225. However, in La(Nb,V)O₄ solid solutions, the TCF decreases from a large positive (+100 ppm °C⁻¹) to a large negative value (−40 ppm °C⁻¹), the opposite trend to that which is typically observed at PTTs. This anomalous behaviour may be further elucidated by undertaking a detailed study of the crystal structure as a function of temperature. In the present work, therefore, we present in situ XRD and Raman data in combination with thermal expansion measurement which are interpreted through Landau theory, Shannon's additive rule, and the Clausius–Mosotti relation. Understanding this behavior might lead to design of temperature stable composite materials in the future.

Materials and methods

Material synthesis

Preparation of the La(Nb_0.9V_0.1)O₄ ceramic was described in detail in our previous work.²¹

Material characterization

Room temperature XRD patterns were acquired using a Bruker D2 Phaser in the 2θ range of 10–70°, with a step size of 0.02. In situ XRD patterns were collected using a Siemens D5000 diffractometer from 30–500 °C using Pt foil as the holder for high temperature measurements. Results were analyzed by the Rietveld profile refinement method, using the FULLPROF program. In situ Raman spectra were obtained with a Renishaw Raman microscope (model InVia) using a 532 nm solid state (100 mW) laser and a Linkam stage (model THMS600). Dielectric properties measurements were performed on sintered ceramics, diameter ∼ 10 mm and thickness ∼ 1 mm, coated with gold using an LCR (Agilent E4980A) and homemade heating system from 25 to 680 °C at 10 kHz, 100 kHz, 250 kHz and 1 MHz with a heating rate of 1 °C min⁻¹.

Results and discussion

In situ XRD patterns of the La(Nb_0.9V_0.1)O₄ ceramic in the temperature range 30–500 °C and cell parameters as a function of temperature are shown in Fig. 1(a) and (b). At room temperature, La(Nb_0.9V_0.1)O₄ crystallized with a monoclinic fergusonite structure (I2/c), with V⁵⁺ ions substituting for Nb⁵⁺. As the temperature increased, some characteristic peaks such as (121) and (130), (002) and (200) converged and merged into a single peak at ∼350 °C, indicating a continuous structural transition from a monoclinic fergusonite structure to a tetragonal scheelite structure (I4₁/a). The cell parameter a decreased with temperature while c increased and became equal to a at 350 °C, commensurate with a linear decrease in β from 93° to 90°, Fig. 1(b). All data are therefore consistent with the premise that ∼10 mol% V⁵⁺ substitutes for Nb⁵⁺, decreasing the distortion of the BO₄ tetrahedra, and lowering the ferroelastic phase transition temperature from 480 °C to 350 °C for undoped LaNbO₄ and La(Nb_0.9V_0.1)O₄, respectively.

Fig. 1 (a) In situ XRD patterns of the La(Nb_0.9V_0.1)O₄ ceramic from 30–500 °C. (b) Cell parameters as a function of temperature. (c) Cell volume and thermal expansion vs. temperature. (d) Schematic of the change in the crystal structure projected along the b axis. (e and f) Experimental (circles) and calculated (line) XRD profiles for La(Nb_0.9V_0.1)O₄ at room temperature (R_p = 8.34%, R_wp = 11.5%, and R_exp = 6.52%) and 400 °C (R_p = 10.9%, R_wp = 14.9%, and R_exp = 9.84%). (The short vertical lines below the patterns mark Bragg reflections. The bottom continuous line is the difference between the observed and the calculated intensity.)

Fig. 1(c) shows the cell volume and thermal expansion data of La(Nb_0.9V_0.1)O₄ as a function of temperature. As the temperature increased from 25 °C to 300 °C, the cell volume increased linearly from 331.19 ų to 336.19 ų corresponding to a gradient of +56 ppm °C⁻¹. The cell volume further increased to 337.53 ų at 500 °C, but the gradient decreased to +20 ppm °C⁻¹, suggesting a structural phase transition at ∼350 °C. Thermal expansion coefficients also followed the same trend (Fig. 1(c)), abruptly changing from +15.5 ppm °C⁻¹ to +11.4 ppm °C⁻¹ at the proposed PTT. Fig. 1(d) is a schematic illustrating the change in the crystal structure along the b axis. In the fergusonite structure, B site ions (Nb,V) are located in the center of distorted tetrahedra with two B–O bond lengths, resulting in different values of a and c, and a β angle >90 degrees. Above 350 °C, the B–O bond lengths in the tetrahedra become equal and the tetrahedral distortion disappears, coincident with β approaching 90 degrees. Cell refinements of fergusonite- and scheelite-structured La(Nb_0.9V_0.1)O₄ at room temperature and 400 °C are shown in Fig. 1(e) and (f), respectively. The refined lattice parameters of La(Nb_0.9V_0.1)O₄ at room temperature are a = 5.23654(7) Å, b = 11.6033(4) Å, c = 5.50762(4) Å, and β = 92.894 (4) ° with the space group I2/c (15) using data (ICSD # 81616) from Machida et al.⁴⁷ The refined lattice parameters of scheelite La(Nb_0.9V_0.1)O₄ at 400 °C are a = c = 5.3781(5) Å, b = 11.6783(7) Å with a space group I4₁/a (88) from (ICSD # 37139) reported by David.⁴⁸ The atomic fractional coordinates and structural details are listed in Tables 1 and 2. Clear domains could be observed from the room temperature TEM images of the La(Nb_0.9V_0.1)O₄ ceramic as shown in Fig. S1 in the ESI† and agree well with the XRD data.

Table 1 Refined atomic fractional coordinates from XRD data for the La(Nb_0.9V_0.1)O₄ sample at room temperature and the lattice parameters are a = 5.23654(7) Å, b = 11.6033(4) Å, c = 5.50762(4) Å, β = 92.894 (4) °. The space group is I2/c (15)

Atom	Site	Occ.	x	y	z
La	4e	0.5	0.25000	0.13539	0.00000
Nb	4e	0.45	0.25000	0.61890	0.00000
V	4e	0.05	0.25000	0.61890	0.00000
O1	8f	1.00	0.04142	0.71988	0.28695
O2	8f	1.00	1.02836	0.44614	0.19333

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Table 2 Refined atomic fractional coordinates from the XRD data for the La(Nb_0.9V_0.1)O₄ sample at 400 °C and the lattice parameters are a = c = 5.3781(5) Å, b = 11.6783(7) Å. The space group is I4₁/a (88)

Atom	Site	Occ.	x	y	z
La	4b	0.25	0.00000	0.25000	0.62500
Nb	4a	0.20	0.00000	0.25000	0.12500
V	4a	0.05	0.00000	0.25000	0.12500
O	16f	1.000	0.15639	0.02148	0.20595

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The ferroelastic phase transition from monoclinic fergusonite to tetragonal scheelite is associated with an increase in point group symmetry from 2/m to 4/m and results in merging of two crystal orientation states (S1 and S2) above the PTT. Hence, second-rank strain tensors can be employed to describe these two orientation states caused by the relative ‘monoclinic’ displacements to the paraelastic scheelite phase:^49,50

e_ij(S₂) = Re_ij(S₁)R^T, (3)

where R and R^T are the 90° rotation matrix and its transposition, respectively. As reported by Schlenker et al.,⁵¹ strain tensor components can be calculated from the cell parameters:



where a_m, b_m, c_m and β_m are the cell parameters of the monoclinic phase, and c_t and c_b are the extrapolated tetragonal phase cell parameters. As described by Aizu,⁴⁹ ferroelasticity can be quantified using the spontaneous strain tensors and the two possible orientation states of La(Nb_0.9V_0.1)O₄ are presented as follows:where is the longitudinal strain and ν = e₁₂ is the shear strain. It follows that the magnitude of the spontaneous strain is:

The spontaneous strain of the La(Nb_0.9V_0.1)O₄ ceramic is ∼3.55% at room temperature, approximately half of that of undoped LaNbO₄ ceramic (6.79%).

According to Landau's theory,⁵² the order parameter η (eqn (7)) may be used to describe the deviation from the paraelastic phase:

where T_c is the PTT, (350 °C) and T is temperature. The magnitude of the spontaneous strain of La(Nb_0.9V_0.1)O₄ is proportional to η according to:

e^s = η × k, (8)

where k is a constant (0.03725). The η × k and e^s values as a function of temperature are plotted in Fig. 2. From room to the phase transition temperature, the agreement between η × k and e^s is obtained, confirming that the transition is of second order.

Fig. 2 Magnitude of the spontaneous strain and order parameter η of the La(Nb_0.9V_0.1)O₄ ceramic as a function of temperature.

Group theory predicts that there are 18 Raman active modes for a monoclinic fergusonite structure (I2/a) and the irreducible representation of the modes is:^53,54

Γ = 8A_g + 10B_g + 8A_u + 10B_u, (9)

where A_g and B_g are Raman active while A_u and B_u are IR active. For the tetragonal scheelite structure (I4₁/a), the irreducible representation according to the group theory is given by:^55,56

Γ = 3A_g + 5B_g + 5E_g + 5A_u + 3B_u + 5E_u, (10)

where all the A_g, B_g and E_g are Raman active and all the A_u and E_u are IR active. The correlation of the representations is at Γ points of the I2/a and I4₁/a space groups. The phase transition in La(Nb_0.9V_0.1)O₄ may be described as a proper ferroelastic with strain as the primary order parameter, dominated by a soft acoustic phonon (marked Q in Fig. 3a). Based on Landau's theory,⁵⁴ω_Q below the PTT (T_C) is given as follows:where ω_Q0 is the frequency at T_C, δc′₀ is a spontaneous shear strain parameter, and T₀ is the temperature at which the ferroelastic phase becomes unstable. ω_Q decreases linearly with temperature in the ferroelastic phase but remains constant in the paraelastic phase, which agrees with the experimental results, Fig. 3b, where ω_Q0 is ∼90 cm⁻¹. For BiVO₄, the ferroelastic → paraelastic phase transition is driven by a temperature-dependent B_g optic mode coupled to the acoustic soft mode as described by Pinczuk et al.^37,57 In contrast to BiVO₄, no soft optical mode has been observed from room temperature to 500 °C, which defines the phase transition in LaNbO₄ to be purely ferroelastic with strain as the sole order parameter.^54,58 Hence, the Lyddane–Sachs–Teller (LST) relation is not followed.

Fig. 3 (a) Raman shifts of La(Nb_0.9V_0.1)O₄ from 25–500 °C and (b) selected modes as a function of temperature.

ε _r and dielectric loss of the La(Nb_0.9V_0.1)O₄ ceramic as a function of temperature at different frequencies (10 kHz, 100 kHz, 250 kHz, 1 MHz and 8.5 GHz) are shown in Fig. 4. Different from BiVO₄ ferroelastic ceramics and other ferroics as shown in Fig. 5b, an anomalous ε_r minimum value was observed at 10 kHz, 100 kHz, 250 kHz, and 1 MHz. Due to the limitation in microwave dielectric measurement, we did not obtain the wide temperature microwave ε_r spectrum but the present data show an apparent decrease of permittivity vs. temperature, which gives a large positive TCF value. Compared with ε_r, there is no abnormality observed from dielectric loss as shown Fig. 4(b). In the microwave region, polarizability is the sum of both ionic and electronic components. Shannon⁵⁹ suggested that the molecular polarizability (α) of complex substances may be estimated by summing α of the constituent ions which for La(Nb_0.9V_0.1)O₄ is:

α_{La(Nb0.9V0.1)O4} = α_La³⁺ + 0.9 × α_Nb⁵⁺ + 0.1 × α_V⁵⁺ + 4α_O²⁻ = 17.98 ų, (12)

where the ionic polarizabilities of La³⁺, Nb⁵⁺, V⁵⁺ and O²⁻ are 6.07 ų, 3.97 ų, 2.92 ų and 2.01 ų, respectively.⁵⁹ Considering the Clausius–Mosotti (C–M) relation,⁶⁰where V is the cell volume (331.19/4 = 82.8 ų). The calculated ε_r is 31.1, much larger than the measured value (∼20) at room temperature. As reported by Tsunekawa et al.,^40,44,53 BO₄ tetrahedra are distorted in the fergusonite structure. The distorted tetrahedra have reduced B–O bond lengths, dampened B–O lattice vibrations and thereby decreased polarizability. Furthermore, macroscopic polarizability also includes additional terms related to the crystal structure and local anisotropy. As reported by Feteira et al.,⁶¹ polarizabilities of lanthanides (Ln) were derived from the rare-earth aluminates system and it became evident that Ln (e.g. La³⁺ = 4.68 ų) has lower values than reported by Shannon.⁵⁹

Fig. 4 (a and b) ε_r and dielectric loss of the La(Nb_0.9V_0.1)O₄ ceramic as a function of temperature at different frequencies (10 kHz, 100 kHz, 250 kHz, 1 MHz and 8.5 GHz).

Fig. 5 (a) Calculated dielectric constant of the La(Nb_0.9V_0.1)O₄ ceramic on assumptions of fixed and linear increasing polarizabilities and (b) schematic of ε_r of typical electro-ceramics vs. temperature.

The C–M relationship indicates that the ε_r of a specific compound is determined both by the cell volume and molecular polarizability. For La(Nb_0.9V_0.1)O₄, as the temperature increased, the cell volume increased linearly below and above 350 °C but with different gradients. Based on the assumption that the molecular polarizability does not change with temperature, ε_r, calculated using eqn (13), is plotted in Fig. 5a which reveals a linear decrease below and above 350 °C but at different gradients. There is therefore an anomaly at 350 °C but not a minimum value of ε_r. However, if we assume that the molecular polarizability increases with temperature and follows a simple linear relation

α_{La(Nb0.9V0.1)O4} = α₀ + (T − T_R) × k, (14)

where α₀ is the room temperature molecular polarizability, 17.975 ų, T_R is room temperature and k (0.00075) is a temperature-dependent constant; the combined effect of the cell volume and molecular polarizability vs. T gives a minimum value of ε_r at the PTT as shown in Fig. 5a. Although this is a rough calculation, it gives a clear explanation for the dielectric minimum of the La(Nb_0.9V_0.1)O₄ ceramic at the PTT, at which point a decrease in thermal expansion coefficient occurs. In Fig. 5b, we summarize the possible curves of ε_rvs. T for a ferroelectric, relaxor, antiferroelectric, ferroelastic, paraelectric and linear dielectric material. The purely ferroelastic character and the sudden decrease in thermal expansion coefficient for La(Nb_0.9V_0.1)O₄ are anomalous compared with conventional ferroics and dielectrics.

Conclusions

The La(Nb_0.9V_0.1)O₄ ceramic was determined by in situ XRD analysis to undergo a ferroelastic phase transition from a monoclinic fergusonite structure to a tetragonal scheelite structure at ∼350 °C. Raman analysis identified strain as the sole order parameter with a value of 3.55% at room temperature, almost half of that of the pure LaNbO₄ ceramic. At the PTT, there was an abrupt change of the thermal expansion coefficient from +15.5 ppm °C⁻¹ to +11.4 ppm °C⁻¹, related to the anomalous change in the cell volume. Assuming a linear increase in polarizability, the minimum value of ε_r at the PTT for La(Nb_0.9V_0.1)O₄ was predicted from the Clausius–Mosotti relation and Shannon's additive rule. Compared with ferroelectrics, relaxors, antiferroelectrics, ferroelastics, paraelectrics and linear dielectrics, the behaviour of ε_r in La(Nb_0.9V_0.1)O₄vs. temperature is anomalous and may have novel applications in temperature stable composite ceramics.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Key Research and Development Program of China (Grant 2017YFB0406301), the Sustainability and Substitution of Functional Materials and Devices EPSRC (EP/L017s563/1), the National Natural Science Foundation of China (51972260, 52072295), the State Key Laboratory of Electrical Insulation and Power Equipment (Grant EIPE19210), the Fundamental Research Funds for the Central University, and the 111 Project of China (B14040).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0qi00981d

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